It has been shown that the stochastic gravitational waves (GW's) produced from a cosmological phase transition can be fully characterized by the
knowledge of two primary parameters [1]}, which are defined as
\(\alpha =\frac{\epsilon (T_{\ast })}{\rho _{\rm rad}(T_{\ast })}~ {\rm and}~\frac{\beta }{H_{\ast }}=T_{\ast }\frac{d}{dT}\left.\left( \frac{S_3(T)}{T} \right)\right|_{T=T_{\ast }},\) 
